Under the collective influence of channel multi-path dispersion, Inter-Symbol Interference and Multiple Access Interference, it becomes a key of that the multi-user detection is practical or not, that how to depress the complexity of the multi-user detection cancellation algorithm, namely the de-correlation method, to acceptable degree. A received symbol vector can be expressed as the sum of a noise vector and the product that a transmitted symbol vector D left multiply by a channel correlation matrix R. Among the algorithm of demodulating the received symbol vector and getting the estimation {circumflex over (D)} of the transmitted symbol, the most complex step is getting the inverse matrix R−1 of the channel correlation matrix R. For example, usually existing technology adopts the following method: in downlink spreading factor is SF=16. Assuming there are K users in one time slot and 1≦K≦16, in each of the data part, there are K*N data symbols altogether, each user has N=22 data symbols. Let the nth transmitted data symbols of all the K users beD(n)=(d1(n), d2(n), d3(n), . . . dk(n)), n=1, . . . , K  (1)
The symbol sequence of each user consists of N elements with intervals Ts. The elements are taken from a complex alphabet (1,j,−1,−j). Each data symbols of user K is multiplied by the user specific signature sequence. The specific signature sequence is expressed as:C(k)=(c1(k), c2(k), . . . , cQ(k))T, k=1, . . . , K  (2)
Here [·]T means vector/matrix transposition. The user specific signature sequence consists of Q chips at chip interval T c that is equal to Ts/Q. Each of the K channels is characterized by its discrete impulse response. The discrete impulse response of the kth channel is expressed as:H(k)=(h1(k), h2(k), . . . , hw(k))T, k=1, . . . , K  (3)
The discrete impulse response consists of W samples at chip rate interval Tc. The channel impulse response is assumed to be unchanged during one time slot.
It is very obviously that ISI arises when W>1, at one time, MAI arises due to channel distortion and non-orthogonal symbol C(k). The combined channel impulse response is defined by the convolution:B(k)=(b1(k), b2(k), . . . , bQ+W−1(k))T=C(k)*H(k), k=1, . . . ,K  (4)
The received sequence e is obtained at the chip rate. It is a sum of K sequences, each of length (N·Q+W−1), that are assumed to be arrive synchronously, perturbed by an noise sequence with same length:n=(n1,n2, . . . , nN·Q+W−1)T  (5)
The received sequence can be written ase=(e1, e2, . . . eN·Q+W−1)T=A·D+n  (6)
With transmitted data vectorD=(D(1), D(2), . . . , D(N))T={d1(1), d2(1), . . . dK(1), . . . d1(n), d2(n), . . . , dK(n), . . . d1(N), d2(N), . . . ,dK(N)}T=(d1, d2, . . . , dKN)T  (7)
Where d1(n), d2(n), . . . dk(n) is the nth symbol of all the K users, anddjdef=dk(n); j=k+K·(n−1), k=1, . . . K, n=1 . . . N  (8)
With the matrix
                                                        A              =                              (                                  a                  ij                                )                                      ;                          i              =                              1                ⁢                                  …                  ⁡                                      (                                                                  N                        ·                        Q                                            +                      W                      -                      1                                        )                                                                                ,                      j            =                          1              ⁢                                                          ⁢              …              ⁢                                                          ⁢                              K                ·                N                                                    ⁢                                  ⁢                              a                                                            Q                  ⁡                                      (                                          n                      -                      1                                        )                                                  +                1                            ,                              k                +                                  K                  ⁡                                      (                                          n                      -                      1                                        )                                                                                =                      {                                                                                                      B                      l                                              (                        k                        )                                                              ,                                                                                        when                    ⁢                                          {                                                                                                                                                                                                    n                                  =                                                                      1                                    ⁢                                                                                                                                                  ⁢                                    …                                    ⁢                                                                                                                                                  ⁢                                    N                                                                                                  ,                                                                  k                                  =                                                                      1                                    ⁢                                                                                                                                                  ⁢                                    …                                    ⁢                                                                                                                                                  ⁢                                    K                                                                                                                              ⁢                                                                                                                                                                                                                                                                                      1                              =                                                              1                                ⁢                                                                                                                                  ⁢                                …                                ⁢                                                                                                                                  ⁢                                                                  (                                                                      Q                                    +                                    W                                    -                                    1                                                                    )                                                                                                                                                                                                                                                                                                          0                    ,                                                                    other                                                                                        (        9        )            
The received sequence e has to be processed to obtain a decision on the transmitted data symbol D under the assumption that the user-specific signature sequences C(k) and the channel cross-correlation H(k), k=1 . . . K are known at receivers.
At the same time zero-forcing method is used to eliminate MAI and ISI. It is based on minimizing∥A{circumflex over (D)}−e∥2  (10)
Here {circumflex over (D)} is the estimation of transmitted symbols of all the K users. So{circumflex over (D)}=(AHA)−1AHe=D+(AHA)−1AHn  (11)
Here [·]H means Hermit transposition and AH e is the output of match filter, (AHA)−1AHn is noise term. Above {circumflex over (D)} contains desired output D and noise, without MAT and ISI. Its covariance matrix δ2(AHA)−1 gives the correlation of the noise term. Generally, the variance of the noise term is more than the noise term which is obtained because of using match filter method. The SNR per-symbol at the output of the de-correlation is equal toγ(k, n)=1/δ2[(AHA)−1]i,j; j=n+N·(k−1), k=1 . . . K, n=1 . . . N  (12)
LetR=AHA  (13)
Then (Eq. 11) becomes{circumflex over (D)}=(R)−1(RD+AHn)=D+(R)−1AHn  (14)
Because the difficulty exists in the matrix inversion operation of R, the calculation burden in TD-SCDMA system is bigger.